Verb: run up against Meaning: Encounter problems, often unexpected They RAN UP AGAINST a lot of opposition to the construction.
Verb: rub up against Meaning: Touch someone in a sensual or sexual way The cat RUBBED UP AGAINST my leg purring.
Verb: run against Meaning: Oppose, make difficulties Opinion is RUNNING AGAINST his policies and he has very little support.
Verb: lash out against Meaning: Criticise something strongly The press has LASHED OUT AGAINST the policy.
Verb: hold out against Meaning: Try to reject The staff are HOLDING OUT AGAINST the plans to reduce the workforce.